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[lemon square]

Design a program that will allow the user to select from the following :
[1] Math algorithms
[2] Figures
[3] Exit

[1]Math algorithms

a. Euclidean Algorithm
In number theory, the Euclidean algorithm is used for finding the greatest common divisor for two integers a and b (not zero) is based on the following fact:
If r is the remainder when a is divided by b, then gcd (a,b) = gcd (b,r).
See the following Pseudocode:
Euclid(a,b) {
while (b not 0) {
interchange(a,b)
b := b mod a
}
return(a)
}

b. The Ulam Sequence
A mathematician named Ulam proposed generating a sequence of numbers from any positive integer n (n > 0) as follows:
• If n is 1, stop.
• If n is even, the next number is n/2.
• If n is odd, the next number is 3*n + 1.
• Continue with this process until reaching 1.
Ex: an input of 3 gives ->10 ->5 -> 16 ->8 -> 4 -> 2 ->1

c. Fibonacci Series
Fibonacci numbers was invented by Leonardo of Pisa (Fibonacci). He defined fibonacci numbers as a growing population of immortal rabbits. Series of Fibonacci numbers are: 1,1,2,3,5,8,13,21,...
The Fibonacci sequence is 0,1,1,2,3,5,8,13,… where the first two terms are 0 and 1, and each term thereafter is the sum of the two preceding terms; that is Fib[n]=Fib[n-1] + Fib[n-2]. Display the Fibonacci series: example, if n=6, the program should display the value 0,1,1,2,3,5.

d. Fermat Little test
If 2^N modulo N = 2 then N has a high probability to be a prime number.
Ex:
let N=11 (we know that 11 is a prime).
2^11 mod 11 = 2048 mod 11 = 2, then N has a high probability to be a prime number.

Using this information, design a program to list all prime numbers that are less than 100.

Shapes
a. Print a rectangle. Read a height and width and print a rectangle with that height and width. This example output has height 3 and width 7.
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b. Print a triangle. Read a number and print a triangle of that size. This example is of size 6.
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c. Print a rectangle outline. Read a height and width and print a rectangle that looks like the one below. This example has a height of 5 and width of 7. You might choose one of two approaches to this problem.
1. Break it down into three problems: a line of stars; lines consisting of a star, blanks, and a star; and again a line of stars.
2. At each position write either a star or blank. Use an if statement to test for first or last row of first or last column, in which case a star is printed, otherwise print a blank.

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[webJose]

Sorry, you need to do your own homework. Code as much as you can, then post specific questions here about specific parts that you are having trouble with.